A little statistical mechanics for the graph theorist

DOI10.1016/j.disc.2010.03.011zbMath1223.05125arXiv0804.2468OpenAlexW2103717946MaRDI QIDQ973134

Laura Beaudin, Joanna A. Ellis-Monaghan, Robert Shrock, Greta Pangborn

Publication date: 28 May 2010

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.2468

zbMATH Keywords

Monte Carlo simulationIsing modelPotts modelstatistical mechanicschromatic polynomialTutte polynomial

Mathematics Subject Classification ID

Graph polynomials (05C31) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (26)

Chromatic zeros on hierarchical lattices and equidistribution on parameter space ⋮ The many facets of the Estrada indices of graphs and networks ⋮ A general method for computing Tutte polynomials of self-similar graphs ⋮ Edge cut splitting formulas for Tutte-Grothendieck invariants ⋮ Exact results on Potts model partition functions in a generalized external field and weighted-set graph colorings ⋮ Unnamed Item ⋮ Characterizing partition functions of the vertex model ⋮ On the Potts model partition function in an external field ⋮ The Tutte polynomial of some matroids ⋮ On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field ⋮ Unnamed Item ⋮ Unnamed Item ⋮ q-plane zeros of the Potts partition function on diamond hierarchical graphs ⋮ Tutte polynomial of the Apollonian network ⋮ Modifications of Tutte–Grothendieck invariants and Tutte polynomials ⋮ Galois groups of chromatic polynomials ⋮ A note on recognizing an old friend in a new place: list coloring and the zero-temperature Potts model ⋮ Functional relations on anisotropic Potts models: from Biggs formula to the tetrahedron equation ⋮ The Tutte-Potts connection in the presence of an external magnetic field ⋮ The behavior of Tutte polynomials of graphs under five graph operations and its applications ⋮ Tutte polynomials of vertex-weighted graphs and group cohomology ⋮ Characterizing partition functions of the spin model by rank growth ⋮ Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs ⋮ Interpretations of the Tutte polynomials of regular matroids ⋮ Gibbs measures of Potts model on Cayley trees: A survey and applications ⋮ Spanning tree generating functions for infinite periodic graphs L and connections with simple closed random walks on L

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